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Anti-gerrymandering formulae

A well known curse of many representative democracies is gerrymandering. People in power draw the districts to assure they will stay in power. There are some particularly ridiculous cases in the USA.

I was recently pointed to a paper on a simple, linear system which tries to divide up a state into districts using the shortest straight line that properly divides the population. I have been doing some thinking of my own in this area so I thought I would share it. The short-line algorithm has the important attribute that it's fixed and fairly deterministic. It chooses one solution, regardless of politics. It can't be gamed. That is good, but it has flaws. Its district boundaries pay no attention to any geopolitical features except state borders. Lakes, rivers, mountains, highways, cities are all irrelevant to it. That's not a bad feature in my book, though it does mean, as they recognize, that sometimes people may have a slightly unusual trek to their polling station.
The main problem with it is that people can overstate the problems with it. Attempts to stop gerrymandering will face strong opposition from the powerful figures who created it in the first place. By definition, they have political power and will work to protect it. As such, to make this happen, there must be no vaguely credible arguments against the system which can be used by the gerrymanderers. That's a tall order, because it's amazing what classes as vaguely credible.

My own thoughts have been based on a principle I will call "non-concavity." That means we seek to not have concave (inward curving) borders on our districts. Here's a rough rule:

For any district, no line between any two points within the district may leave the district, except at a county border.

This requires a district be entirely convex, except another district can intrude into it along a county border. The short-line
algorithm discussed above meets this condition, in fact it meets it with state borders as the only concavities allowed. I suggest a county border as a proxy for many of the other borders we would like to use, including city borders, rivers, mountains, lakes or interstate highways. There may be a better set of borders to allow concavity on -- "rivers and freeways" makes some sense. Mountain ridges seem important but it's harder, but not impossible to write a nice definition.

Some gerrymandering is still possible here. My proposal allows complex snakes of counties, so they may be too small. And indeed, whatever gerrymandering can be done will be done so this deserves more thought. However, most representative systems are intended to provide some amount of representation based on true geographic and social commonalities, so using groups of counties may still have merit.

There is one other tweak I would add to the rule that is a bit hard to write out but is probably needed. We want to allow concavities caused by a single piece of property, so that we can draw the borders along property lines. As such we would say that no line between points in the district may cross a single deeded property which does not itself belong to, or border on the district. Or alternately, "no line between two properties within the district that do not form part of the district border may pass out of the district." This allows rough, crinkly edges along property lines -- which may get visibly crinkly in rural areas -- but should not allow a great deal of manipulation.

All of these methods (and indeed today's crazy lines) require a detailed, property by property census and fancy computerization. But we have that today.

There are other systems, some of which have been used, for example in Connecticut. What matters of course is not simply what the best system is, but what can be sold to the voters against the imaginary objections of the powerful. (That's why I don't like my property line exception very much, as it makes it harder to explain, compared to my basic rule which is very simple to write, and any fool can test against it with a map and a ruler.)

Comments

Gerrymandering is an embarrassment for any country which calls itself democratic.
If, say, Milosovic had suggested such a system in the former Yugoslavia, the
collective consciousness of the world would have cried "whom are you trying to
fool". The real problem is the myth that those elected somehow "represent their
district". Except in cases of pork-barrelling (which also should be eliminated),
that's probably no longer true. It might have been true back in the old days, but
it's not today. And what about the people who didn't vote for the person who got
elected? Who represents them?

The only truly democratic system is proportional representation. A party gets x
percent of the vote and they get x percent of the seats in the parliament or
whatever. It never ceases to amaze me that people deem any other system democratic.
(Of course, proportional representation must deal with rounding errors and perhaps
a threshold, but these are small problems compared to the problems of a
first-past-the-post system, only one of which is gerrymandering.)

Sure, there are deeper problems, but you can't get there from here. Change in the system has to come in baby steps that the public will buy, ideally state by state.

States with public initiatives, and states with state governments who feel they lose through gerrymandering can vote for a better system, and start the trend. Then they can move on to the next thing, a prefferential ballot or similar.

The straight-line algorithm certainly creates plausible and impressive-looking results for such a simple rule.

Another idea, that might wind up in practice being a little like multi-member districts: don't define district boundaries, but rather 'home points' for each seat. Let any voter vote in their choice of one of the N closest-homed seats. This needs more modelling, but my hunch is even if you let partisans place the points as aggressively as possible, simple planar geometry would prevent them from contriving many safe seats from arbitrary placement. (Also, the placing of 'home points' might be very amenable to an automated process.)

Fair pie-cutting algorithms might also help; perhaps something like: If N districts are needed, the dominant party gets free rein to create 3*N equal districts; then the minority party chooses which groupings of 3 become the real districts. Again, more modelling necessary but shenanigans in creating unbalanced phase 1 mini-districts might tend to strengthen the hand of the minority party in phase 2.

Unfortunately an 1842 law requires single member districting. (Very little of the districting rules are in the constitution, in fact prior to this many states did send their reps via total state vote.)

The pie system I think gives too much recognition to the parties. Of course the parties are in total control under the current system, so it's an improvement, but I would rather remove all party control. Party control pushes for incumbency.

Indeed, I like a mathematical algorithm because it doesn't encourage incumbency. My system tries to limit it, but not completely -- that's a flaw balanced by the fact that I think you could get there from here.

A nice little essay I read showed the dangers of even convexity under party choice. Imagine a state with 2 districts which is mostly red on the north and blue on the south. If you divide it with a horizontal line, north from south, you get two safe districts. If you divide it with a vertical line, east from west, you get 2 volatile districts which swing with the undecided and independent voters. Quite a difference from a fairly aribtrary choice.

The house is the place where minority views are supposed to be a bit stronger, at least in states with 4 or more reps. If a highly environmentalist area wants to elect a lone green, it can happen -- and does happen in many countries. If the 2 dominant parties control it, this won't happen.

...have to sign off on any reform, so giving them formal recognition in the process may be a feature not a bug.

The parties aren't *strictly* for incumbency: they're for 'safe party seats', which just happens to work out that way once any old crook gets elected to a safe seat for his party. The incumbents are of course for incumbency. So perhaps the teams that play the pie-cutting game are made up of *former* party officeholders as a slight countermeasure. (We may actually want people who are party loyalists rather than officeholder suckups for best game results.)

The degenerate two-district case is interesting, but if one party has even a slight advantage, their desire for a chance at winning two seats may sometimes outweigh their desire for one safe seat and one guaranteed loss. It would seem to depend on other governance choices -- how much of a premium is a governing majority versus a seat at the table?